Session-22.pdf - Derivations and Languages We define the...

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Derivations and Languages: We define the language generated by grammar G= (V,T,P,S) , if A → β is a production of P and α, γ are any strings in ( VUT) * then α A γ → α β γ . Where α A γ is directly derives α β γ in grammar G. Relation meaning ? 𝑮 ? 𝒐𝒓 ? ? β is obtained from α by one application of some production ? ? 𝒐𝒓 ? ? β is obtained from α by applying of some productions ? 𝒊 ? β is obtained from α by exactly i steps (or i no. of productions) Derivations of a string can be specified into two ways: 1. Leftmost derivation : A derivation 𝑨 𝒘 is called a leftmost derivation if we apply a production only to the leftmost variable at every step. It is denoted by using the relation ?? and for one or more steps, respectively. 2. Rightmost derivation : A derivation 𝑨 𝒘 is called a rightmost derivation if we apply a production only to the rightmost variable at every step. It is denoted by using the relation 𝒓? and for one or more steps, respectively. Sentential Forms: Derivations from the start symbol produce strings that have special role. We call these
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